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Majority-vote model on a random lattice.

F W S Lima1, U L Fulco, R N Costa Filho

  • 1Departamento de Física, Universidade Federal do Piauí, 57072-970 Teresina, Piauí, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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We studied the critical properties of a voting model on disordered random lattices. Our findings show unique critical exponents and a critical noise parameter of 0.117, differing from standard lattice models.

Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • The majority vote model is a key tool for understanding opinion dynamics and phase transitions.
  • Investigating models on random lattices with disorder is crucial for realistic system analysis.

Purpose of the Study:

  • To calculate the stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder.
  • To determine the critical exponents gamma and beta for this specific model.
  • To identify the critical noise parameter (q(c)).

Main Methods:

  • Utilized Monte Carlo simulations.
  • Employed finite size analysis techniques.
  • Focused on the isotropic majority vote model with quenched disorder.

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Main Results:

  • Calculated critical exponents gamma and beta.
  • Found these exponents differ from those of the Ising model and the majority vote model on a square lattice.
  • Determined the critical noise parameter to be q(c) = 0.117 ± 0.005.

Conclusions:

  • The isotropic majority vote model on disordered random lattices exhibits distinct critical behavior compared to non-disordered or regular lattice models.
  • The identified critical exponents and noise parameter provide valuable insights into the phase transitions of systems with quenched disorder.